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Godel's Incompleteness TheoremsOxford University Press USA. 1992.An introduction to the work of the mathematical logician Kurt Godel, which guides the reader through his Theorem of Undecidability and his theories on the completeness of logic, the incompleteness of numbers and the consistency of the axiom of choice.
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12A beginner's guide to mathematical logicDover Publications. 2014.Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompletenes…Read more
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8Gödel's Incompleteness TheoremsIn Lou Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell. 2017.At the turn of the century, there appeared two comprehensive mathematical systems, which were indeed so vast that it was taken for granted that all mathematics could be decided on the basis of them. However, in 1931, Kurt Gödel surprised the entire mathematical world with his epoch‐making paper which begins with the following startling words: The development of mathematics in the direction of greater precision has led to large areas of it being formalized, so that proofs can be carried out accor…Read more
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8A beginner's further guide to mathematical logicWorld Scientific. 2017.More on propositional and first-order logic -- More on propositional logic -- More on first-order logic -- Recursion theory and metamathematics -- Some special topics -- Elementary formal systems and recursive enumerability -- Some recursion theory -- Doubling up -- Metamathematical applications -- Elements of combinatory logic -- Beginning combinatory logic -- Combinatorics galore -- Sages, oracles, and doublets -- Complete and partial systems -- Combinators, recursion, and the undecidable -- W…Read more
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10Theory of Formal SystemsPrinceton University Press. 1961.This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.
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20J. R. Shoenfield. Undecidable and creative theories. Fundamenta mathematicae, vol. 49 no. 2 , pp. 171–179Journal of Symbolic Logic 32 (1): 123. 1967.
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13Vladeta Vučković. Mathematics of incompleteness and undecidability. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 13 , pp. 123–150 (review)Journal of Symbolic Logic 37 (1): 195-196. 1972.
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24Rudy Rucker. Mind tools. The five levels of mathematical reality. Houghton Mifflin Company, Boston1987, viii + 328 pp (review)Journal of Symbolic Logic 53 (4): 1254-1255. 1988.
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10Exact Separation of Recursively Enumerable Sets Within TheoriesJournal of Symbolic Logic 25 (4): 362-362. 1960.
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118First-order logicSpringer Verlag. 1968.This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as ...
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34Theories with Effectively Inseparable NucleiMathematical Logic Quarterly 6 (15-22): 219-224. 1960.
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8An Unfortunate DualistIn David J. Chalmers (ed.), Philosophy of Mind: Classical and Contemporary Readings, Oup Usa. 2002.
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31What is the Name of this Book?: The Riddle of Dracula and Other Logical PuzzlesPhilosophical Review 88 (3): 496. 1979.
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29Quine Willard Van Orman. Methods of logic. Revised edition, Henry Holt and Company, Inc., New York 1959, xx + 272 pp (review)Journal of Symbolic Logic 24 (3): 219-220. 1959.
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What Is the Name of This Book? The Riddle of Dracula and Other Logical PuzzlesCritica 13 (38): 126-130. 1981.
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55Diagonalization and self-referenceClarendon Press. 1994.This book presents a systematic, unified treatment of fixed points as they occur in Godels incompleteness proofs, recursion theory, combinatory logic, semantics, and metamathematics. Packed with instructive problems and solutions, the book offers an excellent introduction to the subject and highlights recent research.
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18To Mock a Mockingbird: And Other Logic PuzzlesOxford University Press. 1985.In this entertaining and challenging collection of logic puzzles, Raymond Smullyan-author of Forever Undecided-continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time.
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15A Generalization of Intuitionistic and Modal LogicsJournal of Symbolic Logic 42 (2): 316-317. 1977.
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72Some new double induction and superinduction principlesStudia Logica 49 (1). 1990.Some new double analogues of induction and transfinite recursion are given which yields a relatively simple proof of a result of Robert Cowen, [2] which in turn is a strengthening of an earlier result of Smullyan [1], which in turn gives a unified approach to Zorn's Lemma, the transfinite recursion theorem and certain results about ordinal numbers.
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45Undecidability and recursive inseparabilityZeitschrift fur mathematische Logik und Grundlagen der Mathematik 4 (7-11): 143-147. 1958.